Geometric optimization of intruded cavities on the basis of Constructal theory

In this work the optimization of the shape of open cavities that intrude into a solid conducting wall is considered. The basic global constraint is that the solid construct must fit into a given volume. The hot spots are located along the solid conducting wall which generates heat uniformly and it is insulated on the external perimeter, while the cavity represents an heat sink. As open cavity this region is called ‘‘inverted fin’’ or ‘‘negative fin’’. The aim of this paper is to prove the relation between the maximization of global performance in terms of heat removal and the morphing architecture of a cavity that intrudes into the conductive solid. The maximization of the rate of heat transfer in a given volume has led to design new structures for several engineering applications. In this way, the optimization has been conducted according to the Constructal principle of optimal distribution of imperfections, in order to achieve as much as possible an optimized flow architecture. Depending on the particular matter of the cavity that for the present purpose can be convective or isothermal, its optimal shape varies and its variation can be predicted by the Constructal principle, according to which the optimization of geometry generates a treeshaped structure with several degrees of freedom. Indeed the system, which is composed by the tree-shaped intruded cavity into the solid conductive wall, can vary its dimensions in terms of ratios between steams and tributaries. In this work the tendency by the flows to adopt themselves paths characterized by minimal resistance is demonstrated. In case of isothermal cavity, the tree-shaped structure tends to reduce the hot spot distributed volumes, as a minimal global thermal resistance is observed. This trend is registered for the convective cavity as well, but with different results; indeed, when the cavity admits also a convective heat transfer between internal surfaces and the stream that passes through the cavity, the tree-shaped optimal geometry changes: the steam now penetrates into the solid body and the tributaries extend themselves completely along his whole length.